Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.

A new design of sliding mode control systems

A new sliding mode control technique for a class of SISO dynamic systems is presented in this chapter. It is seen that the stability status of the closed-loop system is first checked, based on the approximation of the most recent information of the first-order derivative of the Lyapunov function of the closed-loop system, an intelligent sliding mode controller can then be designed with the following intelligent features: (i) If the closed-loop system is stable, the correction term in the controller will continuously adjust control signal to drive the closed-loop trajectory to reach the sliding mode surface in a finite time and the desired closed-loop dynamics with the zero-error convergence can then be achieved on the sliding mode surface. (ii) If, however, the closed-loop system is unstable, the correction term is capable of modifying the control signal to continuously reduce the value of the derivative of the Lyapunov function from the positive to the negative and then drives the closed-loop trajectory to reach the sliding mode surface and ensures that the desired closed-loop dynamics can be obtained on the sliding mode surface. The main advantages of this new sliding mode control technique over the conventional one are that no chattering occurs in the sliding mode control system because of the recursive learning control structure; the system uncertainties are embedded in the Lipschitz-like condition and thus, no priori information on the upper and/or the lower bounds of the unknown system parameters and uncertain system dynamics is required for the controller design; the zero-error convergence can be achieved after the closed-loop dynamics reaches the sliding mode surface and remains on it. The performance for controlling a third-order linear system is evaluated in the simulation section to show the effectiveness and efficiency of the new sliding mode control technique.

Exact-estimator-based terminal sliding mode control system design

This paper investigates an estimator-based terminal sliding mode control system. An exact estimator is proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic levitation system to implement the control performance.

Robust fault-tolerant leader-follower control of four-wheel-steering mobile robots using terminal sliding mode

This paper addresses the actuator failure compensation problem of non-linear fourwheel-steering mobile robots based on vehicle kinematics, undergoing both known and unknown failures causing degenerated steering performance or wheels stuck at some observable angles. Terminal sliding mode control technique is used to guarantee the tracking stability infinite time with the presence of actuator fault. Simulation results are given to illustrate the effectiveness of the proposed control scheme. © Institution of Engineers Australia 2012.

Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

DSP-based sliding-mode control for electromagnetic-levitation precise position system

This paper investigates the robust tracking control problem for a bipolar electromagnetic-levitation precise-position system. The dynamic model of the precise-position device is derived by conducting a thorough analysis on the nonlinear electromagnetic forces. Conventional sliding-mode control and terminal sliding-mode control strategies are developed to guarantee asymptotic and finite-time tracking capabilities of the closed-loop system. A lumped uncertainty estimator is proposed to estimate the system uncertainties. The estimated information is then used to construct a smooth uniformly ultimately bounded sliding-mode control. An exact estimator is also proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding-mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic-levitation system to validate the analysis.

Sliding mode control based terminal impact angle constrained guidance laws using dual sliding surfaces

In this paper, sliding mode control theory based guidance laws to intercept non-maneuvering targets at a desired impact angle are presented. The desired impact angle, defined in terms of a desired line-of-sight (LOS) angle, is achieved by selecting the missile's lateral acceleration (latax) to enforce sliding mode on a sliding surface based on this LOS angle. As will be shown, this guidance law does not ensure interception for all states of the missile and the target during the engagement. Hence, to satisfy the requirement of interception at the desired impact angle, a second sliding surface is designed and a switching logic, based on the conditions necessary for interception, is presented that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using non-linear engagement dynamics.

Non-singular terminal sliding mode guidance and control with terminal angle constraints for non-maneuvering targets

In this paper guidance laws to intercept stationary and constant velocity targets at a desired impact angle, based on sliding mode control theory, are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight (LOS) angle, is achieved in finite time by selecting the missile's lateral acceleration (latax) to enforce non-singular terminal sliding mode on a switching surface designed using this desired LOS angle and based on non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles.

Integral terminal sliding mode cooperative control of multi-robot networks

This paper studies the integral terminal sliding mode cooperative control of multi-robot networks. Here, we first propose an integral terminal sliding mode surface for a class of first order systems. Then, we prove that finite time consensus tracking of multi-robot networks can be achieved on this integral terminal sliding mode surface. Simulation results are presented to validate the analysis.

Discrete-time sliding mode control of input-delay systems applied on a power generation system

This paper presents two discrete sliding mode control (SMC) design. The first one is a discrete-time SMC design that doesn't take into account the time-delay. The second one is a discrete-time SMC design, which takes in consideration the time-delay. The proposed techniques aim at the accomplishment simplicity and robustness for an uncertainty class. Simulations results are shown and the effectiveness of the used techniques is analyzed. © 2006 IEEE.

Frequency Domain Characterization Of Sliding Mode Control Of An Inverter Used In DSTATCOM Application

In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Sliding Mode Control-Based Autopilots for Leaderless Consensus of Unmanned Aerial Vehicles

In this brief, decentralized sliding mode controllers that enable a connected and leaderless swarm of unmanned aerial vehicles (UAVs) to reach a consensus in altitude and heading angle are presented. In addition, sliding mode control-based autopilot designs to control those states for which consensus is not required are also presented. By equipping each UAV with this combination of controllers, it can autonomously decide on being a member of the swarm or fly independently. The controllers are designed using a coupled nonlinear dynamic model, derived for the YF-22 aircraft, where the aerodynamic forces and moments are linear functions of the states and inputs.

Impact Time Guidance for Large Heading Errors Using Sliding Mode Control

In this paper, sliding mode control-based impact time guidance laws are proposed. Even for large heading angle errors and negative initial closing speeds, the desired impact time is achieved by enforcing a sliding mode on a switching surface designed by using the concepts of collision course and estimated time-to-go. Unlike existing guidance laws, the proposed guidance strategy achieves impact time successfully even when the estimated interception time is greater than the desired impact time. Simulation results are also presented.